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Component-wise approximate Bayesian computation via Gibbs-like step
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Clarté, Grégoire, Robert, Christian P., Ryder, Robin and Stoehr, Julien (2021) Component-wise approximate Bayesian computation via Gibbs-like step. Biometrika, 108 (3). pp. 591-607. asaa090. doi:10.1093/biomet/asaa090 ISSN 0006-3444.
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WRAP-Component-wise-approximate-Bayesian-computation-Gibbs-like-steps-Robert-2020.pdf - Accepted Version - Requires a PDF viewer. Download (3947Kb) | Preview |
Official URL: https://doi.org/10.1093/biomet/asaa090
Abstract
Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this dimension grows. To tackle this difficulty, we explore a Gibbs version of the Approximate Bayesian computation approach that runs component-wise approximate Bayesian computation steps aimed at the corresponding conditional posterior distributions, and based on summary statistics of reduced dimensions. While lacking the standard justifications for the Gibbs sampler, the resulting Markov chain is shown to converge in distribution under some partial independence conditions.The associated stationary distribution can further be shown to be close to the true posterior distribution and some hierarchical versions of the proposed mechanism enjoy a closed form limiting distribution. Experiments also demonstrate the gain in efficiency brought by the Gibbs version over the standard solution.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Library of Congress Subject Headings (LCSH): | Bayesian statistical decision theory, Bayesian statistical decision theory -- Data processing, Mathematical analysis, Conditional expectations (Mathematics) , Markov processes -- Numerical solutions, Sampling (Statistics) | ||||||||
Journal or Publication Title: | Biometrika | ||||||||
Publisher: | Biometrika Trust | ||||||||
Place of Publication: | Biometrika | ||||||||
ISSN: | 0006-3444 | ||||||||
Editor: | Robert, Christian P. | ||||||||
Official Date: | September 2021 | ||||||||
Dates: |
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Volume: | 108 | ||||||||
Number: | 3 | ||||||||
Page Range: | pp. 591-607 | ||||||||
Article Number: | asaa090 | ||||||||
DOI: | 10.1093/biomet/asaa090 | ||||||||
Institution: | University of Warwick | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Reuse Statement (publisher, data, author rights): | This is a pre-copyedited, author-produced version of an article accepted for publication in Biometrika following peer review. The version of record Grégoire Clarté, Christian P Robert, Robin J Ryder, Julien Stoehr, Component-wise Approximate Bayesian Computation via Gibbs-like steps, Biometrika, , asaa090 is available online at: https://doi.org/10.1093/biomet/asaa090 | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 7 October 2020 | ||||||||
Date of first compliant Open Access: | 4 November 2021 | ||||||||
RIOXX Funder/Project Grant: |
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